More on the dynamics of the symbolic square root map
| Autor: | Jarkko Peltomäki, Markus A. Whiteland |
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| Rok vydání: | 2020 |
| Předmět: |
General Computer Science
Dynamical systems theory 0102 computer and information sciences 02 engineering and technology Type (model theory) Dynamical system 01 natural sciences Square (algebra) Theoretical Computer Science Combinatorics Square root 010201 computation theory & mathematics Product (mathematics) 0202 electrical engineering electronic engineering information engineering 020201 artificial intelligence & image processing Limit set Computer Science::Formal Languages and Automata Theory Word (group theory) Mathematics |
| Zdroj: | Theoretical Computer Science. 806:10-27 |
| ISSN: | 0304-3975 |
| DOI: | 10.1016/j.tcs.2018.08.019 |
| Popis: | In our earlier paper [Peltomaki and Whiteland (2017) [5] ], we introduced a symbolic square root map. Every optimal squareful infinite word s contains exactly six minimal squares and can be written as a product of these squares: s = X 1 2 X 2 2 ⋯ . The square root s of s is the infinite word X 1 X 2 ⋯ obtained by deleting half of each square. We proved that the square root map preserves the languages of Sturmian words (which are optimal squareful words). The dynamics of the square root map on a Sturmian subshift are well understood. In our earlier work, we introduced another type of subshift of optimal squareful words which together with the square root map form a dynamical system. In this paper, we study these dynamical systems in more detail and compare their properties to the Sturmian case. The main results are characterizations of periodic points and the limit set. The results show that while there is some similarity it is possible for the square root map to exhibit quite different behavior compared to the Sturmian case. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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